MasterCard has launched another missile at a Visa rule that will prohibit its members from issuing both associations' debit card brands.

Maestro U.S.A., the affiliate responsible for MasterCard's on-line debit program in the United States, announced last week that it will permit member banks to issue the competing Visa brand, Interlink.

Before the change was approved by the Maestro U.S.A. board, the practice known as duality was permitted only at the holding company level. That meant one subsidiary of a holding company could issue Maestro while Interlink would have to be issued by another.

With both single-bank and holding company duality now permitted for Maestro, MasterCard International rules are now consistent across three key product categories: on-line debit cards, off-line debit cards (Master Money and Visa Check), and credit cards.

"We think the members should have every option available for the way in which they want to compete," Peter S.P. Dimsey, MasterCard's U.S. region president, said in an interview during the Bank Administration Institute's retail delivery systems conference in Phoenix.

MasterCard thus continues to challenge Visa U.S.A.'s rule requiring that dual-issuing members make a choice within a year on all cards except credit cards. Duality has reigned in credit cards since the 1970s, and neither association advocates undoing it.

Visa accepts duality as appropriate for mass-market credit cards. It calls for nonduality in debit and commercial cards on grounds that they are integral parts of deposit relationships, which in its view should have an exclusive and consistent brand image.

MasterCard casts its argument as one for freedom of choice. Some industry observers suspect a more cynical motive: that only through duality can MasterCard close the market-share gap that now favors Visa.

Critics of MasterCard also say that debit card duality would contravene a consent agreement in an antitrust case that forced MasterCard and Visa to abandon plans for a joint debit program, called Entree.

But Arthur D. Kranzley, senior vice president and general manager of debit products at MasterCard International, said he has obtained an opinion from the National Association of State Attorneys General, which brought the suit against Entree, that the current duality policy appears legal.

Mr. Kranzley said that, with the completed overhaul of debit-duality rules and the attorneys general group's opinion, banks may pressure Visa to ease its restrictions.

"MasterCard has always supported duality for its Master- Card-branded products in the United States, and we are pleased to extend this fully to the Maestro brand," Mr. Kranzley said. "We believe it is in the best interest of our members ...POS debit duality promotes innovation and efficiency and will help accelerate the development of POS debit in the United States."

Mr. Dimsey said MasterCard's policy promotes banks' "doing what is best for their customers and their profitability. If you are an interstate bank, why not be able to test two brands in two different markets and the decide which is best?"

There are signs that New York-based MasterCard is gaining in debit cards. Chemical Bank announced Nov. 30 that it would issue Master Money and Maestro in 1995. Bank of New York recently adopted Maestro; Signet Bank of Richmond, Va., is relaunching its point of sale debit program as Master Money; and Fifth Third Bank of Cincinnati has converted from Visa Check to Master Money.

MasterCard also has stepped up consumer education and advertising of its debit programs in the United States, and Mr. Kranzley said card-activation trends are encouraging. Still, the numbers generally favor Visa.

The off-line Visa Check card, formerly Visa Debit, is being issued by 1,200 U.S. institutions, including 300 that launched programs in the first nine months of 1994. Total cards stood at 17.8 million at Sept. 30, up 34% from a year earlier, Visa said.

Master Money has 463 U.S. members and four million cards, according to figures published at the retail delivery systems conference.

Maestro's strong suit is international, where Mr. Kranzley said Visa's Interlink on-line program is not a factor. Maestro International is in 58 countries. About three-fourths of its 109 million live cards are the European Maestro/edc brand.

Maestro U.S.A. reported 9.6 million live cards and 18 million committed, and the cards are usable at 32,000 merchant locations.

Interlink recently surpassed 50,000 merchants, up from 5,000 when Visa acquired the network from major California banks in 1991. At Sept. 30, there were 29 million cards, and Visa projects 80 million by 1998. The program has made its first international signings in Panama, Korea, and Taiwan.

Mr. Kranzley of MasterCard said Interlink still benefits from its "head start" in the West in the 1980s, but he claimed to be "at parity" in new signings.